TSTP Solution File: SET646+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 00:52:51 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   60 (  13 unt;   0 def)
%            Number of atoms       :  271 (  18 equ)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :  351 ( 140   ~; 147   |;  25   &)
%                                         (   7 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  122 (   8 sgn  52   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p21,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p21) ).

fof(p25,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p25) ).

fof(p19,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p19) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ( member(ordered_pair(X1,X2),cross_product(X3,X4))
                  <=> ( member(X1,X3)
                      & member(X2,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p2) ).

fof(prove_relset_1_8,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,set_type)
                 => ( ( member(X3,X1)
                      & member(X4,X2) )
                   => ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_8) ).

fof(p5,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( X3 = singleton(X2)
              <=> ! [X4] :
                    ( ilf_type(X4,set_type)
                   => ( member(X4,X3)
                    <=> X4 = X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p5) ).

fof(p17,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X1,power_set(X2))
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p17) ).

fof(p3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p3) ).

fof(p12,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,subset_type(X1))
          <=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p12) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( ( ~ empty(X3)
        | ~ ilf_type(X4,set_type)
        | ~ member(X4,X3)
        | ~ ilf_type(X3,set_type) )
      & ( ilf_type(esk14_1(X3),set_type)
        | empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( member(esk14_1(X3),X3)
        | empty(X3)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p21])])])])])])])]) ).

fof(c_0_10,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[p25]) ).

fof(c_0_11,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X3,member_type(X4))
        | member(X3,X4)
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ member(X3,X4)
        | ilf_type(X3,member_type(X4))
        | empty(X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p19])])])])])])]) ).

cnf(c_0_12,plain,
    ( ~ ilf_type(X1,set_type)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X5,X6,X7,X8] :
      ( ( member(X5,X7)
        | ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( member(X6,X8)
        | ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ~ member(X5,X7)
        | ~ member(X6,X8)
        | member(ordered_pair(X5,X6),cross_product(X7,X8))
        | ~ ilf_type(X8,set_type)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])])]) ).

cnf(c_0_15,plain,
    ( empty(X2)
    | ilf_type(X1,member_type(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13])]) ).

cnf(c_0_17,plain,
    ( member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X4,set_type)
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,set_type)
               => ! [X4] :
                    ( ilf_type(X4,set_type)
                   => ( ( member(X3,X1)
                        & member(X4,X2) )
                     => ilf_type(singleton(ordered_pair(X3,X4)),relation_type(X1,X2)) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_8]) ).

cnf(c_0_19,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_13])]),c_0_16]) ).

cnf(c_0_20,plain,
    ( member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_13]),c_0_13]),c_0_13])]) ).

fof(c_0_21,negated_conjecture,
    ( ilf_type(esk1_0,set_type)
    & ilf_type(esk2_0,set_type)
    & ilf_type(esk3_0,set_type)
    & ilf_type(esk4_0,set_type)
    & member(esk3_0,esk1_0)
    & member(esk4_0,esk2_0)
    & ~ ilf_type(singleton(ordered_pair(esk3_0,esk4_0)),relation_type(esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).

fof(c_0_22,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ member(X8,X7)
        | X8 = X6
        | ~ ilf_type(X8,set_type)
        | X7 != singleton(X6)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( X8 != X6
        | member(X8,X7)
        | ~ ilf_type(X8,set_type)
        | X7 != singleton(X6)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ilf_type(esk6_2(X6,X7),set_type)
        | X7 = singleton(X6)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ~ member(esk6_2(X6,X7),X7)
        | esk6_2(X6,X7) != X6
        | X7 = singleton(X6)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( member(esk6_2(X6,X7),X7)
        | esk6_2(X6,X7) = X6
        | X7 = singleton(X6)
        | ~ ilf_type(X7,set_type)
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])])])]) ).

fof(c_0_23,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,power_set(X5))
        | ~ ilf_type(X6,set_type)
        | ~ member(X6,X4)
        | member(X6,X5)
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ilf_type(esk10_2(X4,X5),set_type)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( member(esk10_2(X4,X5),X4)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( ~ member(esk10_2(X4,X5),X5)
        | member(X4,power_set(X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])])])])]) ).

cnf(c_0_24,plain,
    ( ilf_type(ordered_pair(X1,X2),member_type(cross_product(X3,X4)))
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    member(esk4_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,plain,
    ( X4 = X2
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | X3 != singleton(X2)
    | ~ ilf_type(X4,set_type)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( member(X1,power_set(X2))
    | member(esk10_2(X1,X2),X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,plain,
    ( empty(X2)
    | member(X1,X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,member_type(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,negated_conjecture,
    ( ilf_type(ordered_pair(X1,esk4_0),member_type(cross_product(X2,esk2_0)))
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    member(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    ( X1 = X2
    | X3 != singleton(X1)
    | ~ member(X2,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_13]),c_0_13]),c_0_13]),c_0_13])]) ).

cnf(c_0_32,plain,
    ( member(esk10_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_13]),c_0_13])]) ).

cnf(c_0_33,plain,
    ( empty(X1)
    | member(X2,X1)
    | ~ ilf_type(X2,member_type(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_13]),c_0_13])]) ).

cnf(c_0_34,negated_conjecture,
    ilf_type(ordered_pair(esk3_0,esk4_0),member_type(cross_product(esk1_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    ( member(X1,power_set(X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(esk10_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_36,plain,
    ( X1 = esk10_2(X2,X3)
    | member(X2,power_set(X3))
    | X2 != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,plain,
    ( ~ empty(cross_product(X1,X2))
    | ~ member(X3,X2)
    | ~ member(X4,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_20]) ).

cnf(c_0_38,negated_conjecture,
    ( empty(cross_product(esk1_0,esk2_0))
    | member(ordered_pair(esk3_0,esk4_0),cross_product(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,plain,
    ( empty(X1)
    | member(esk14_1(X1),X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_40,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk10_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_13]),c_0_13])]) ).

cnf(c_0_41,plain,
    ( esk10_2(singleton(X1),X2) = X1
    | member(singleton(X1),power_set(X2)) ),
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    ( member(ordered_pair(esk3_0,esk4_0),cross_product(esk1_0,esk2_0))
    | ~ member(X1,esk2_0)
    | ~ member(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,plain,
    ( empty(X1)
    | member(esk14_1(X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_13])]) ).

cnf(c_0_44,negated_conjecture,
    ~ empty(esk2_0),
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

fof(c_0_45,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
        | ilf_type(X7,relation_type(X5,X6))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) )
      & ( ~ ilf_type(X8,relation_type(X5,X6))
        | ilf_type(X8,subset_type(cross_product(X5,X6)))
        | ~ ilf_type(X6,set_type)
        | ~ ilf_type(X5,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])])]) ).

fof(c_0_46,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X4,subset_type(X3))
        | ilf_type(X4,member_type(power_set(X3)))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ ilf_type(X4,member_type(power_set(X3)))
        | ilf_type(X4,subset_type(X3))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])])])]) ).

cnf(c_0_47,plain,
    ( member(singleton(X1),power_set(X2))
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    ( member(ordered_pair(esk3_0,esk4_0),cross_product(esk1_0,esk2_0))
    | ~ member(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_49,negated_conjecture,
    ~ empty(esk1_0),
    inference(spm,[status(thm)],[c_0_16,c_0_30]) ).

cnf(c_0_50,plain,
    ( ilf_type(X3,relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_51,plain,
    ( ilf_type(X2,subset_type(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X2,member_type(power_set(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_52,plain,
    ( ilf_type(singleton(X1),member_type(power_set(X2)))
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_47]) ).

cnf(c_0_53,negated_conjecture,
    member(ordered_pair(esk3_0,esk4_0),cross_product(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_49]) ).

cnf(c_0_54,negated_conjecture,
    ~ ilf_type(singleton(ordered_pair(esk3_0,esk4_0)),relation_type(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_55,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_13]),c_0_13])]) ).

cnf(c_0_56,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,member_type(power_set(X2))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_13]),c_0_13])]) ).

cnf(c_0_57,negated_conjecture,
    ilf_type(singleton(ordered_pair(esk3_0,esk4_0)),member_type(power_set(cross_product(esk1_0,esk2_0)))),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_58,negated_conjecture,
    ~ ilf_type(singleton(ordered_pair(esk3_0,esk4_0)),subset_type(cross_product(esk1_0,esk2_0))),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET646+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 23:48:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.018 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 60
% 0.22/1.40  # Proof object clause steps            : 41
% 0.22/1.40  # Proof object formula steps           : 19
% 0.22/1.40  # Proof object conjectures             : 17
% 0.22/1.40  # Proof object clause conjectures      : 14
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 14
% 0.22/1.40  # Proof object initial formulas used   : 9
% 0.22/1.40  # Proof object generating inferences   : 17
% 0.22/1.40  # Proof object simplifying inferences  : 37
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 26
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 6
% 0.22/1.40  # Initial clauses                      : 50
% 0.22/1.40  # Removed in clause preprocessing      : 2
% 0.22/1.40  # Initial clauses in saturation        : 48
% 0.22/1.40  # Processed clauses                    : 308
% 0.22/1.40  # ...of these trivial                  : 17
% 0.22/1.40  # ...subsumed                          : 51
% 0.22/1.40  # ...remaining for further processing  : 240
% 0.22/1.40  # Other redundant clauses eliminated   : 2
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 4
% 0.22/1.40  # Backward-rewritten                   : 8
% 0.22/1.40  # Generated clauses                    : 1441
% 0.22/1.40  # ...of the previous two non-trivial   : 1333
% 0.22/1.40  # Contextual simplify-reflections      : 8
% 0.22/1.40  # Paramodulations                      : 1419
% 0.22/1.40  # Factorizations                       : 10
% 0.22/1.40  # Equation resolutions                 : 12
% 0.22/1.40  # Current number of processed clauses  : 227
% 0.22/1.40  #    Positive orientable unit clauses  : 66
% 0.22/1.40  #    Positive unorientable unit clauses: 0
% 0.22/1.40  #    Negative unit clauses             : 10
% 0.22/1.40  #    Non-unit-clauses                  : 151
% 0.22/1.40  # Current number of unprocessed clauses: 964
% 0.22/1.40  # ...number of literals in the above   : 3288
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 12
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 2670
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 2018
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 41
% 0.22/1.40  # Unit Clause-clause subsumption calls : 436
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 34
% 0.22/1.40  # BW rewrite match successes           : 4
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 25315
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.057 s
% 0.22/1.40  # System time              : 0.005 s
% 0.22/1.40  # Total time               : 0.062 s
% 0.22/1.40  # Maximum resident set size: 4664 pages
% 0.22/23.40  eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.22/23.40  
% 0.22/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.42  eprover: No such file or directory
% 0.22/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.48  eprover: No such file or directory
% 0.22/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------